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Unformatted text preview: BIOMETRICS CSE190 Fall 2006 Assignment 1 Due: October 19, 2006 1. For a single feature, what are the optimal decision regions where: = { 1 , 2 } P(x  1 ) = N(2, 0.5) (Normal distribution) P(x  2 ) = N(1.5, 0.2) P( 1 ) = 2/3 P( 2 ) = 1/3 11 = 0, 12 = 1, 21 = 1, 22 =0 2. Select the optimal decision regions for the above problem when: 11 = 1, 12 = 2, 21 = 3, 22 =4 3 . Problem 2.13 in DHS. In many pattern classification problems one has the option either to assign the pattern to one of c classes, or to reject it as being unrecognizable. If the cost for rejects is not too high, rejection may be a desirable action. Let + = = = = Otherwise c i c j i j i s r j i 1 ,..., 1 , , )  ( Where r is the loss incurred for chosing the (c+1)th action, rejection, and s is the loss incurred for making any substitution error. Show that the minimum risk is obtained if we decide i if P ( i...
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 Fall '06
 Kriegman

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